Prime Type III Factors
arXiv:math/0008146 · doi:10.1073/pnas.220417397
Abstract
We show that for each (0<λ<1), the free Araki-Woods factor of type III(_λ) cannot be written as a tensor product of two diffuse von Neumann algebras (i.e., is prime), and does not contain a Cartan subalgebra.
Cited by in corpus (8)
- Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors
- Bass-Serre rigidity results in von Neumann algebras
- Amalgamated free product type III factors with at most one Cartan subalgebra
- Primeness results for von Neumann algebras associated with surface braid groups
- Notes on Free Probability Theory
- Examples of factors which have no Cartan subalgebras
- Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
- Free quasi-free states and factors of type III (after D. Shlyakhtenko)